Why is my file so much bigger after baking textures and adding an HDRI, and can I reduce it?
First, you can make sure no textures or external data is accidentally packed into Blender by using the File > External Data > Unpack All Into Files function.

Second, Blender keeps orphaned datablocks around until the next time you save the Blender file. So Save the file, close it. And reopen it, doing it a few times can clear any deleted datablocks from the file.

You can also use the File > Save As > Enable Compression setting to make sure the blend file is compressed to save some space. For files larger than a hundred MB, it will take a bit longer to save and open.